Why are documents kept separated when training a text classifier?
Common words should not be ignored.  For instance, there may be a correlation between document classes and whether more indefinite articles like a or an are included or more definite ones like the or this.

Neither is word count is a good substitution for word distribution. (Frequency though it is commonly (not necessarily frequently) used is an incorrect term.  Words do not normally occur periodically in natural language.)  Representing word distribution throughout the concatenated text of multiple documents of a single category.

The distribution of use of individual words and the distribution of language units and word pair proximity may correlate well to document classification, but the linguistic pattern distribution may vary from document to document within the same class, so the distribution of distributions is relevant.  The deviations between distributions is information needed for proper statistical analysis.

In ten documents of differing sizes, the distribution of words may differ for some words and correlate for others.  Concatenating them hides the distribution of distributions.  From an information theory perspective, concatenating and totaling across the concatenation would represent an information loss with respect to separate documents analysis.

The naive Bayesian machinery produces the most reliable categorization when all information is integrated into the probability calculations.